Q. What do the crafter-related attributes Craftsmanship, Magic Craftsmanhip, and Control each do?
A. Among recipes in the game, there are those for which the rate of progress and chance of success are increased by higher Craftsmanship, and those for which they are determined by Magic Craftsmanship. Control helps to reduce the occurrence of aetherial sparking (see below), and exerts its influence over both types of recipes just mentioned.

All recipes, however, have set attribute requirements. Attempting a recipe with attributes below those required will result in lessened progress and quality, even for successful actions.

Having higher Control help reduce the chance that your synthesis light would get the spark when you fail the attempt.

Craftsmanship & Mg.Craftsmanship will influence how you tend to get fail/success on a recipe. I usually try to boost Craftsmanship. As of now there's a real solid information about which recipe require Craftsmanship and which one require Mg.Craftsmanship. So safe bet would be to boost both and balance them, or boost either one and switch over if you notice dramatic rate of failure.

Output, on the other hand, is for gatherer (Disciple of the land). From my observation, higher output means you can gather for more attempts from one spot before having to move and look for next spot.